1 Introduction
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Reference generator
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High level controller
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Low level controller
2 Torque-vectoring control framework
2.1 Reference generator
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\({K_{us}}\) is the understeer gradient and it represents the initial slope of the curve. For example, a value of \(K_{us}\) lower than for the baseline vehicle results in a more reactive vehicle (closer to a neutral behaviour).
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\({a^*_y}\) is the lateral acceleration limit of the linear region.
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\({a_{y,MAX}}\) is the maximum achievable lateral acceleration.
2.2 High level controller
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\(0 < c_1 \le 100 \) because \(c_1 > 0\) guarantees a bell-shaped f, while excessive values of \(c_1\) are avoided as they would provoke a transition of f from 0 to 1 in an too tight range of \(I_Y\), resulting in a too fast transition from \(M_{z,SSC}\) to \(M_{z,TC}\) according to Eq. 7, in turn implying large oscillations of \(M_z\) that are undesired
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\(-6 \le c_2 \le -3\) because \(c_2 \le -3\) guarantees \(f(0)=1\), while excessively negative values of \(c_2\) are avoided as they enlarge the range of \(I_Y\) for which \(f \approx 1\), and a too large range would not allow \(M_{z,TC}\) to intervene
2.3 Low level controller
2.4 Driving modes
Driving mode | \(K_{us}\) | \(\beta _{MAX}\) (°) | Yaw moment definition | Torque distribution parameters |
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Normal | \(K_{us,b}\) | 5 | Reference tracking | \(\sigma _L\), \(\sigma _R\) |
Sport | \( \frac{3}{4}K_{us,b}\) | 5 | Reference tracking | \(\sigma _L\), \(\sigma _R\) |
Energy efficiency | – | – | Energy optimisation | \(\varDelta T_{LR}\), \(\sigma _L\), \(\sigma _R\) |
2.4.1 The energy efficiency mode
2.5 Measurements and sensors
Measurement | Symbol(s) | Sensor |
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Yaw rate | r | Inertial Measurement Unit (IMU) |
Longitudinal and lateral accelerations | \(a_x\), \(a_y\) | Inertial Measurement Unit (IMU) |
Wheel speed | \(\omega _{ij}\) | Wheel speed sensors |
Steering wheel angle | \(\delta _{sw}\) | Steering wheel angle sensor (LWS) |
Range | Angular speed | Resolution | CAN Speed |
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\(\pm 780^{\circ }\) | up to \(1000 ^{\circ }\)/s | \(0.1 ^{\circ }\) | 500 kbaud |
Range | Filter | Resolution | CAN Speed | |
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Gyroscope | \(\pm 300^{\circ }\)/s | 70 Hz (configurable) | 0.1°/s | 500 kbaud |
Accelerometer | \(\pm 50\) m/s2 | 70 Hz (configurable) | 0.1 m/s2 | 500 kbaud |
3 Results and discussion
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6 DOF for the car body, i.e. 3 displacements and 3 rotations (yaw, pitch and roll).
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4 DOF for the wheel vertical displacements.
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4 DOF for the wheel rotations with respect to their hub axis.
Symbol | Name and unit | Value |
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m | Mass (kg) | 1580 |
\(J_z\) | Moment of inertia, vertical axis (kg m2) | 2210 |
a | Front semi-wheelbase (m) | 0.977 |
l | Wheelbase (m) | 2.7 |
\(\tau \) | Motor transmission ratio (–) | 8.92 |
\(R_w\) | Wheel radius (m) | 0.336 |
w | Track width (m) | 1.592 |
h | Centre of mass height (m) | 0.55 |
\(C_{1}\) | Front axle cornering stiffness (N/rad) | \(2.355 \times 10^5\) |
\(C_{2}\) | Rear axle cornering stiffness (N/rad) | \(2.196 \times 10^5\) |
3.1 Steady-state manoeuvre: ramp steer
3.2 Transient manoeuvres
3.2.1 Open loop: step steer
3.2.2 Closed loop: double lane change
3.2.3 Closed loop: mild slalom
Driving mode | Ramp steer | Mild slalom | ||
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\(\varDelta P_{loss,tot}\) (%) | \(\varDelta E_{loss,tot}\) (%) | |||
Low \(a_y\) | Medium \(a_y\) | High \(a_y\) | ||
Normal mode | − 0.08% | − 0.60% | − 4.28% | + 2.82% |
Sport mode | + 1.58% | + 7.21% | + 0.69% | + 7.01% |
Energy efficiency mode | − 0.23% | − 0.84% | − 7.51 % | − 1.40% |
4 Conclusions
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The developed integrated torque-vectoring framework ensures a smooth cooperation between the three main blocks of a TV controller, and it allows to achieve multiple control objectives at the same time.
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The driving mode selector allows the driver to modify the vehicle behaviour based on his/her preferences, including modes that modify the vehicle cornering response in different ways, or a specific mode that maximises the vehicle energy efficiency.
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The Energy efficiency mode makes the most of the actuation redundancy, focusing solely on minimising the vehicle energy consumption. It should be used together with an appropriate driving style from the driver.
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The high level controller provides a trade-off between yaw rate tracking and sideslip angle tracking, prioritising the latter in safety-critical conditions, and mitigating excessive sideslip angle rates to enhance vehicle safety.
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The low level controller allows to increase the driving range of the electric vehicle by maximising the vehicle energy efficiency, even when the torque-vectoring controller is mainly used to modify the vehicle handling behaviour.